On the cardinality of matrices with prescribed rank and partial trace over a finite field

被引：1

作者：

Balasubramanian, Kumar ^{[1
]}

Kaipa, Krishna ^{[2
]}

Khurana, Himanshi ^{[3
]}

机构：

[1] IISER Bhopal, Dept Math, Bhopal 462066, Madhya Pradesh, India

[2] IISER Pune, Dept Math, Pune 411008, Maharashtra, India

[3] Harish Chandra Res Inst, Dept Math, Prayagraj 211019, Uttar Pradesh, India

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2025年 / 704卷

关键词：

Rank; Trace; Cardinality; Generating function; DEGENERATE WHITTAKER MODELS; LINEAR-GROUPS; GAUSS SUMS;

D O I：

10.1016/j.laa.2024.10.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let F be the finite field of order q and M(n, n, r, F ) be the set of n x n matrices of rank r over the field F . For alpha E F and A E M(n, n, F ), let Z alpha A,r = {X X E M(n, n, r, F ) Tr(AX) AX ) = alpha } . In this article, we solve the problem of determining the cardinality of Z alpha A,r . We also solve the generalization of the problem to rectangular matrices. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页码：35 / 57

页数：23

共 50 条

[41] A note on adjacency preservers on hermitian matrices over finite fields
Orel, M.
FINITE FIELDS AND THEIR APPLICATIONS, 2009, 15 (04) : 441 - 449
[42] Determinant Formula and Trace Formula for Some Finite Rank Perturbation of Heisenberg Commutation Relation
Daoxing Xia
Integral Equations and Operator Theory, 2008, 60 : 573 - 590
[43] Determinant formula and trace formula for some finite rank perturbation of Heisenberg commutation relation
Xia, Daoxing
INTEGRAL EQUATIONS AND OPERATOR THEORY, 2008, 60 (04) : 573 - 590
[44] Invariants of trace forms over finite fields of characteristic 2
Fitzgerald, Robert W.
FINITE FIELDS AND THEIR APPLICATIONS, 2009, 15 (02) : 261 - 275
[45] On non-full-rank perfect codes over finite fields
Romanov, Alexander M.
DESIGNS CODES AND CRYPTOGRAPHY, 2019, 87 (05) : 995 - 1003
[46] On non-full-rank perfect codes over finite fields
Alexander M. Romanov
Designs, Codes and Cryptography, 2019, 87 : 995 - 1003
[47] Cocyclic Butson Hadamard matrices and codes over Zn via the trace map
Pinnawala, N.
Rao, A.
FINITE FIELDS AND APPLICATIONS, 2008, 461 : 213 - 228
[48] THE ENHANCED PRINCIPAL RANK CHARACTERISTIC SEQUENCE OVER A FIELD OF CHARACTERISTIC
Martinez-Rivera, Xavier
ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2017, 32 : 273 - 290
[49] Combinatorial properties of the enhanced principal rank characteristic sequence over finite fields
Dukes, Peter J.
Martinez-Rivera, Xavier
SPECIAL MATRICES, 2022, 10 (01): : 166 - 179
[50] On the minimal rank in non-reflexive operator spaces over finite fields
Pazzis, Clement de Seguins
LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 462 : 126 - 132

← 1 2 3 4 5 →